Locally repairable codes with strict availability from linear functions
نویسندگان
چکیده
منابع مشابه
Linear Locally Repairable Codes with Random Matrices
In this paper, locally repairable codes with all-symbol locality are studied. Methods to modify already existing codes are presented. Also, it is shown that with high probability, a random matrix with a few extra columns guaranteeing the locality property, is a generator matrix for a locally repairable code with a good minimum distance. The proof of this gives also a constructive method to find...
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In recent years, several classes of codes are introduced to provide some fault-tolerance and guarantee system reliability in distributed storage systems, among which locally repairable codes (LRCs for short) play an important role. However, most known constructions are over large fields with sizes close to the code length, which lead to the systems computationally expensive. Due to this, binary...
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When a node in a distributed storage system fails, it needs to be promptly repaired to maintain system integrity. While typical erasure codes can provide a significant storage advantage over replication, they suffer from poor repair efficiency. Locally repairable codes (LRCs) tackle this issue by reducing the number of nodes participating in the repair process (locality), with the cost of reduc...
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We consider the locally repairable codes (LRC), aiming at sequential recovering multiple erasures. We define the (n, k, r, t)SLRC (Sequential Locally Repairable Codes) as an [n, k] linear code where any t(≤ t) erasures can be sequentially recovered, each one by r (2 ≤ r < k) other code symbols. Sequential recovering means that the erased symbols are recovered one by one, and an already recovere...
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We show that locally repairable codes (LRCs) can be list decoded efficiently beyond the Johnson radius for a large range of parameters by utilizing the local error correction capabilities. The new decoding radius is derived and the asymptotic behavior is analyzed. We give a general list decoding algorithm for LRCs that achieves this radius along with an explicit realization for a class of LRCs ...
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ژورنال
عنوان ژورنال: Science China Information Sciences
سال: 2018
ISSN: 1674-733X,1869-1919
DOI: 10.1007/s11432-018-9444-4